Drill bits with internal cooling capabilities are still not employed in stone machining practices within shop floor environments. Therefore, a conventional industrial drill bit used in stone machining was subject to a redesign wherein an axial cooling channel was machined throughout its body. A comparison was drawn between the standard drill bit without cooling capabilities and the redesigned drill bit, which used compressed air as a cooling medium. The experiment was performed by drilling three types of stone samples varying in hardness with nine combinations of cutting speed and feed rate. During the machining process, two types of process signals were continuously measured—namely, cutting forces and vibrations. Additionally, the cutting edges of the drill bits were inspected after a specific number of drilling cycles using a vision system. The primary objective of this study was to compare the cutting forces and tool wear dynamics achieved by those two drill bits. Furthermore, the usage of vibration signals in the classification of stone hardness during machining with an internally cooled drill bit was additionally analyzed. The results of this study unveiled improvement in minimizing cutting forces, vibrations, and the intensity of tool wear when utilizing an internally cooled drill bit. Even though the machining system generally exhibited lower vibrations, vibration signals again demonstrated commendable efficacy in classifying stone hardness.